The manuscript proposes and evaluates a real-time algorithm for estimating eye gaze angle based solely on single-channel electrooculography (EOG), which can be obtained directly from the ear canal using conductive ear moulds. In contrast to conventional high-pass filtering, we used an algorithm that calculates absolute eye gaze angle via statistical analysis of detected saccades. The estimated eye positions of the new algorithm were still noisy. However, the performance in terms of Pearson product-moment correlation coefficients was significantly better than the conventional approach in some instances. The results suggest that in-ear EOG signals captured with conductive ear moulds could serve as a basis for light-weight and portable horizontal eye gaze angle estimation suitable for a broad range of applications. For instance, for hearing aids to steer the directivity of microphones in the direction of the user’s eye gaze.

January
Real-time estimation of horizontal gaze angle by saccade integration using in-ear electrooculography
Ľubo sÏ HlaÂ dek 0 1
Bernd Porr 1
W. Owen Brimijoin 0 1
0 Medical Research Council/Chief Scientist Office Institute of Hearing Research - Scottish Section, Glasgow, United Kingdom, 2 School of Engineering, University of Glasgow , Glasgow , United Kingdom
1 Editor: Manabu Sakakibara, Tokai University , JAPAN
The manuscript proposes and evaluates a real-time algorithm for estimating eye gaze angle based solely on single-channel electrooculography (EOG), which can be obtained directly from the ear canal using conductive ear moulds. In contrast to conventional high-pass filtering, we used an algorithm that calculates absolute eye gaze angle via statistical analysis of detected saccades. The estimated eye positions of the new algorithm were still noisy. However, the performance in terms of Pearson product-moment correlation coefficients was significantly better than the conventional approach in some instances. The results suggest that in-ear EOG signals captured with conductive ear moulds could serve as a basis for lightweight and portable horizontal eye gaze angle estimation suitable for a broad range of applications. For instance, for hearing aids to steer the directivity of microphones in the direction of the user's eye gaze.
-
Funding: This work was supported by grants
from the Oticon Foundation, the UK Medical
Research Council [grant nos. U135097131 and
MC_UU_00010/4], and the Chief Scientist Office
(Government of Scotland). The funders had no role
in study design, data collection and analysis,
decision to publish, or preparation of the
manuscript.
Introduction
Following a conversation in noisy environments can be challenging for hearing aid users
because hearing aids amplify noise together with the target signal. Thus, hearing aids are often
equipped with directional microphones, which attenuate background noise and amplify only
the signals originating in front of the listener. In a typical conversation, however, the
conversational partners can be outside the amplification pattern and the hearing impaired people adopt
a strategy to follow a talker with the eyes [1±3]. The hearing devices do not take into account
the eye movements; and therefore, it would be desirable that hearing prostheses were able to
adapt according to the direction of eye gaze. Some authors have suggested that using eye gaze
angle to steer hearing aid directional microphones could be of benefit to a listener [
4,5
]. How
eye gaze is measured, however, remains an open question. The most reliable methods for
mobile eye tracking involve cameras mounted on glass frames, but the cameras obstruct the
field of view [6], and not every hearing aid user is willing to wear glasses.
A viable candidate for measuring eye gaze angle is electrooculography (EOG) which
measures an electrical signal that arises from the rotation of electrically charged eyeballs.
Consequently, electrodes placed in the vicinity of the eyes can measure these potentials, and
the magnitude of these potentials depend on the eye gaze angle. EOG has many practical
applications including wheelchair control [
7,8
], activity recognition [
9,10
], retinal function testing
[
11,12
], sleep stage classification [13], or as a general gaze control interface [14±16]. It is also
known as an artifact of electroencephalography (EEG) [
17
]. However, its full potential for
hearing aids (or indeed any mobile applications) has not been fully recognized, mainly because
the EOG is typically measured by using large obtrusive electrodes that are attached to the sides
of the head. Due to the electrical properties of the body, however, EOG can be measured
anywhere on the head, although its magnitude varies with the electrode placement. When
measured in peri-orbital positions it usually has values 8±33 μV/ 1Ê of visual angle, and around
3 μV /1Ê can be measured inside the ear canals [
11,18
]. This finding suggests that eye
movements can be analysed by hearing aids with nothing more than conductive ear-moulds.
Eye movements are seen in the EOG signal as a change of the potential across two
electrodes placed either horizontally or vertically around the eyeballs. The analysis of EOG is
usually based on detection of saccades, fixations, and blinks [10,14±16,19±21]. Saccades are the
most common type of eye movement, and they are characterized by a rapid change of the eye
position between two relatively stable fixation points. They produce very distinct patterns in
the EOG voltage, which are relatively easy to detect because the deflections have magnitudes
which are above the usual high-frequency noise level, and they are short in duration.
Microsaccades are tremor-like movements during fixation periods but they produce relatively small
EOG signals that are difficult to detect. Other types of eye movements such as smooth pursuit,
vestibulo-ocular reflex, vergence movement, nystagmus, or optokinetic reflex could be
analysed by EOG, but they are not in the focus of this study.
Saccade detection algorithms often claim near perfect detection rates. However, the
performance of these algorithms vary with the quality of the EOG recording, which is influenced by
electrode types, the electrode placements, lighting conditions [
11
], and the degree of physical
activity. Most methods are based on the analysis of the derivative of the EOG signal and
subsequent classification. The derivative function can be understood as a high-pass (HP) filter with
a cut-off frequency proportional to the sampling rate. The output of the derivative is usually
very noisy, and therefore various approaches proposed ways to increase the signal to noise
ratio. The method [
14
] used a rule-based algorithm to classify the derivative output as a
saccade if the derivative changed the sign. The methods [
15,20
] employed probabilistic
featurebased classification using Gaussian mixture models on the derivative output. The methods
[10] and [
16
], instead of the derivative, analysed parameters of continuous wavelet
transformation. The transformation parameters are then used as an input into a neural network or nearest
neighbour classifier. Yet another method [
19
] analysed the second derivate (acceleration) of
the EOG signal. The saccades were then detected by thresholding the acceleration values, and
the threshold was adapted based on the previous measurements. Although these methods
perform well, they have not considered the saccade magnitude as a predictor and using this
predictor can possibly improve the performance of the detection algorithm.
Obtaining the saccade magnitude from EOG will, however, require a calibration of the
EOG signal to the eye gaze angle [
16
]. Under ideal conditions, the relationship is
straightforward: EOG = constant sin(eye angle) for all eccentricities, and this linear relationship holds
for small and intermediate eccentricities. However, the actual relationship depends on the
placement of electrodes, properties of body tissue, the shape of the head and other factors.
Various techniques detect saccades, blinks, and fixations, but only a few estimate the actual
eye gaze angle from EOG. For instance, the method [
22
] estimated eye gaze using a
comparison of EOG signals from multiple electrodes in different locations around the eyes. The
method took into account the non-linear relationship of the signals from different
2 / 24
measurements sites, which enabled it to cancel out the errors. The method reported the
accuracy of about 4Ê. Such an approach, however, is inapplicable to a setting with only one EOG
channel. In another work [
23
], an external video was used to calibrate the system. The method
was based on a comparison of the saliency maps [
24
] and the EOG signal. This technique
achieved an estimation error of about 15Ê. However, this method is also not suitable for
applications without an external video source. In summary, the state-of-the-art technology [
6
] does
not provide a solution to estimate the actual gaze position from a single-channel recording.
The reason is that EOG has previously been considered for the detection of only relativeÐnot
absoluteÐchanges of eye position. In this paper, we aim to challenge this view by assuming
that eye position can be restored by integrating past saccades. Such an approach will lead to
noisy predictions, but we argue that the level of noise will be acceptable for some applications.
The EOG signal is often polluted by various sources of noise [
12
], which are usually difficult
to eliminate by simple filtering. The most dominant noise component in the EOG is the direct
current (DC) drift. The drift can be characterized as a low-frequency noise (less than 1 Hz)
with unstable spectral structure and with magnitudes up to several hundred mV. DC drift is
inherent to any process involving electrodes attached to the skin [
25
], and it arises from the
imbalance of the half-cell potentials of the two electrodes. When skin conductance changes
(e.g., when sweat is released), the salt concentrations of the electrode gels change, and any
differences between the two electrodes result in a slowly changing DC potential. The voltage
changes that correspond to the actual EOG are small, and they ride on top of this large DC
component (Fig 1). Although it is theoretically possible to decrease the drift in laboratory
environments [
12
], this is not expected in real settings. The second largest source of noise is muscle
activity [
10
]. These artifacts are stronger if the electrodes are placed closer to the muscles
generating the electrical activity such as eye muscles, facial muscles, jaw muscles, neck muscles,
tongue, or limbs. For example, vertical EOG electrodes pick up eye blinks whereas horizontal
electrodes are less affected or not affected at all [
21
]. These artifacts are present in any type of
muscle activity, and they can be seen as a broadband noise with magnitudes similar or greater
than EOG. Electrical activity of the brain itself has virtually no impact on the EOG because of
its very low amplitudes in comparison to the EOG signal. The synchronized activity of specific
Fig 1. Raw in-ear EOG. (A,C) Two samples of 22-minute recordings of raw in-ear EOG. (B,D) Detailed view of the
EOG waveform on a scale of 20 seconds. Straight solid lines denote the position of the visual targets. Small rectangles
in the panels A and C indicate where the detailed views were taken from. The scale of y-axis in the zoomed in-panels B
and D was kept fixed to 2 mV, x-axis was fixed to 20 s, and it shows actual time during the experiment.
3 / 24
brain regions could potentially influence EOG, but again only at very low amplitudes and not
at the locations where EOG is recorded. Finally, noise may arise from external sources
including environmental and powerline noise which are picked up by the wires of the measurement
device. These are typically limited to a narrow spectral region (e.g., 50 Hz or 60 Hz) and can
easily be overcome by notch filters. Although the noise negatively impacts the quality of the
EOG signal, transient events, such as saccades, are less error-prone to external noise due to
their transitory nature. Saccade detection is therefore relatively reliable, even if the signal is
corrupted.
The primary aim of this manuscript is to determine whether eye gaze direction can be
estimated from the in-ear EOG recordings. Specifically, we aim to test a saccade integration
algorithm and compare it to the output of the high-pass filtering approach. The saccade
integration algorithm is a novel approach to estimate the actual eye gaze angle. It relies on the
assumption that the variance of the eye gaze direction can be explained mainly by the saccadic
movement, and only to a small extent by other types of eye movements. In this work, the
saccade integration scheme has the following assumptions: 1) every eye movement can be
characterized as an instantaneous step-like change of location, and all other types of eye movements
can be ignored, 2) the eye is perfectly still during the fixation period, 3) there exists an
approximately linear relationship on a short time scale between the change of the EOG signal and the
change of the eye position [
16
], 4) noise related to the estimation of saccade magnitude has a
normal distribution, 5) eye gaze is constrained by physical limitations, and 6) the head remains
still. In future, the sixth assumption could be omitted, and the information about head
movements could be used to enhance the estimation of eye gaze angle [
26
]. However, in this initial
work, we decided to keep the head fixed. The model prediction is that the performance of the
integration scheme will be better than working directly on the HP-filtered EOG.
For the remainder of the paper, we define these two approaches as:
· EOGHP, where the HP-filtered EOG is directly used for eye gaze angle estimation;
· SACCINT, where the HP-filtered EOG is fed into a saccade detector, and then the result is
integrated.
This manuscript describes the eye gaze estimation scheme using in-ear EOG recordings
and compares the output to the actual eye position monitored by a video-based eye tracker.
Methods
Participants
Seven normal- or corrected-to-normal-sighted human participants participated in the
experiment. One participant could not perform the task with the eye tracker, and one participant
was equipped with different type of electrodes. The data of the five remaining participants
were used in the subsequent analysis. This study was approved by the West of Scotland
Research Ethics Service. The participants were members of the Institute of Hearing Research,
and they provided written informed consent.
Setup and procedures
The experiment was conducted in a testing booth (4.6 m x 4.1 m x 2.5 mÐl x w x h) with lights
turned off during the experiment. The acoustically treated room is one of the booths which are
commonly used for auditory experiments. The participants were seated directly in the front of
a 40º LCD screen (Samsung, UE40ES5500) at distance of 77 cm from the screen to the eyes
(Fig 2A). The participants' heads were not restrained or supported, but the participants were
4 / 24
Fig 2. Experimental apparatus. (A) Schematics of the experimental procedure. (B) The participant was equipped with the mobile
bio-amplifier (blue box) attached to the headband and the video-based eye tracker. (C) Detail of the in-ear electrodes.
instructed to remain still and fixate on a small white dot (1Ê of visual angle) on a grey
background at the height of their eyes. The position of the dot was drawn from a pseudorandom de
Bruijn sequence [
27
] of 11 possible target locations that spanned from the left to right margins
of the screen, covering approximately ± 30.5Ê of visual field. The dots changed their position
after a pseudorandom interval of 0.8±1.2 s. The sequence was constructed so that all positions
were equally represented and the transition between each possible pair of the positions
occurred exactly 11 times, which led to 113 (1331) total target presentations. The actual
measurement period lasted about 22 minutes (excluding preparation). In the offline analysis, the
measurement was split into a training period, in which the parameters of the model were
estimated, and a testing period, in which the performance of the system was assessed.
A DC-coupled differential bio-amplifier (Attys, Glasgow Neuro LTD, UK) and a
videobased eye tracker (Pupil Labs, Berlin, Germany) [
28
] that served as ground truth were used for
the recording (Fig 2B). The bio-amplifier was equipped with a low-noise 24-bit sigma-delta
AD converter and a Bluetooth transmitter which transmitted the measurements to the
experimental computer at a sampling frequency (fs) of 83.34 Hz. When a measurement was
unavailable, the previous value was used instead. Two disposable conductive ear moulds (Fig 2C)
were made of ER1-14A ear tips (Etymotic Research, Elk Grove Village, IL, USA) and
conductive thread (Electro Fashion, Kitronic, Nottingham, UK). The electrodes were attached to the
bio-amplifier by 20 cm long non-shielded cables, and a small portion of electrode gel was put
on the tip of the electrodes before insertion into the ear canal. The ground electrode was
connected to the forehead with a regular medical grade Ag-Cl electrode. The bio-amplifier was
held near the head using an adjustable plastic headband sourced from the inside of a
construction hard hat. The ground truth eye tracker was connected to a dedicated Linux computer
running eye tracker software (Pupil Capture, v0.7.5). The data from the ground truth eye tracker
were collected for both eyes at 60 Hz with a resolution of 800 x 600 pixels. The eye tracker
software directly outputted the eye gaze angle using a 3D eye model. The eye tracker computer
transmitted the measurements via the local network to the experimental computer, where all
recordings were kept for offline analysis. The experimental computer executed custom Matlab
(v8.6.0, Natick, USA), Psychtoolbox [29±31] and Python (v3.5.1) scripts, which controlled the
pace of the experiment.
Ground truth
The eye data outputted by the eye tracker software were calibrated to the actual positions using
histograms of all measurements. Subsequently, a linear transformation was applied to match
5 / 24
the measurements with the positions of the targets. The resulting eye gaze angle was computed
as a mean of the angles from the left and right eyes. The eye tracker and the bio-amplifier data
were then temporally aligned using timestamps recorded by the eye tracker and the
timestamps obtained by the experimental computer during the recording of the bio-amplifier data.
For the purpose of the analysis, saccades from the ground truth were detected using the
EyeMMV toolbox [
32
] with the following settings: minimum saccade duration was set to 50
ms, spatial parameters were set to x = 0.06 and y = 0.05 of the tracker units (normalized to
0±1) using the option `3s' (i.e., the fixation cluster is defined as three standard deviations from
the centre). In order to evaluate the system, the saccades obtained from the eye tracker were
matched to the saccades estimated from the EOG data. Two saccades were matched if they
were temporally closest to each other (sooner or later) and if
jsaccEOGj < j1:5
saccGTj  10
1
where |saccEOG| is the magnitude of the EOG saccade and |saccGT| is the magnitude of the
saccade obtained from the ground truth. That means that the computed magnitude of the saccade
had to be less than 1.5 times the magnitude of the ground truth saccade plus 10Ê (i.e., only the
saccades of approximately equal magnitudes could be matched). These corrections were used
to ensure correct matching when the EOG and the ground truth signals were not perfectly
aligned in time, which was a side effect of the wireless transmission. In order to minimize the
problems related to the delays and to make sure that the matching procedure worked as
expected, matching was visually checked. We concluded that the delays between the EOG and
the eye tracker had only a small impact and the delay could not influence the difference
between the methods which are compared in this manuscript.
Saccade integration scheme
The proposed EOG to eye gaze algorithm, SACCINT (Fig 3), used a single-channel EOG signal
as an input. Ground truth measurements served to calibrate the system before the actual
testing. The algorithm outputted eye gaze angle with a theoretical delay of up to 200 ms, which
corresponded to half of the temporal window (see below) and the delay due to the HP filter.
The analysis was run offline, though the algorithm can be run in real-time. In the first step of
the scheme, the HP-filtered signal of the length of the temporal window was used to estimate
three parameters of a non-linear model of a saccade, which was an s-shaped function:
magnitude Sx, gain Sg, and temporal offset So. These parameters were evaluated to confirm the
saccade detection, and they were then used in subsequent integration. The saccades were
identified when the time offset parameter So crossed the midline of the temporal window and
when the magnitude of the signal deflection Sx was in a range defined by a minimum (Nx,min)
and a maximum of 70Ê. In the integration step, the saccades were represented as noisy
measurements using a Gaussian probability density function (PDF). Subsequently, they were
integrated over time. The integration had two steps. First, the mean of a new PDF was obtained as
a sum of the previous mean and the magnitude of the new saccade. The variance was increased
by a constant Nm which represented noise related to the measurement. In the second step, the
PDF was clipped at the fixed boundaries ±EAnax. The algorithm used one more parameter
Ci [Ê/mV], which defined the linear relationship between the change of EOG and the change
of the horizontal eye gaze angle. Ci was estimated for each participant (index i). The
parameters Ci, Nm, and Nx,min were calibrated for the whole dataset during the training phase using
the ground truth measurements.
6 / 24
Fig 3. Model scheme.
https://doi.org/10.1371/journal.pone.0190420.g003
7 / 24
Fig 4. Step response of the IIR HP Butterworth filters as a function of half-power frequency.
High-pass filtering
The bio-amplifier readings were HP filtered with a second-order Butterworth filter with the
cut-off frequency fHP. The purpose of the filtering was to remove as much of the low-frequency
noise as possible but at the same time preserve information regarding eye position.
Fig 4 shows the step response of HP filters with cut-off frequencies between 0.01 and 0.06
Hz for up to 6 seconds (6 seconds is a reasonable time for a very long off-axis fixation). The
HP filter with cut-off frequency of 0.01 Hz reduces the step signal only by ~9% after 1 second
(which was the typical duration of the visual target in this experiment) and it does not cross 0
even after 6 seconds. On the other hand, the HP filter with 0.06 Hz cut-off reduces the signal
by ~47% after 1 second and crosses zero at less than 3 seconds. While the first example would
affect a typical eye movement to a small extent, the latter example would change the slopeÐ
particularly for long fixations.
At this HP filtering stage of the algorithm, the traditional EOGHP algorithm took this signal
and calculated the eye angle directly. The SACCINT algorithm, however, further processed the
HP-filtered signal as described in the following section.
Non-linear fit
The next step of the SACCINT algorithm was to fit the non-linear function to the HP-filtered
signal. The signal was used to estimate the parameters of the simple saccadic model, which
consisted of the s-shaped function:
f u  Sx tanh Sg u  So
AVG Sx tanh Sg u  So
2
The fit was obtained using a standard non-linear fitting procedure with constraints [
33
]
with a limit of 20 iterations, and the objective function defined as the least square error.
The parameters were constrained with the following values: So = <-136 ms, 136 ms>,
Sg = <-150,150>, Sx = (0 mV, 1,05 x (max(xEOG)-min(xEOG))) /2 mV> where xEOG is the
8 / 24
EOG signal in the temporal window. The initial estimates for the three parameters were
obtained as a weighted average of the previously estimated value and a pseudo randomly
selected value from the above intervals with weights 0.95 and 0.05, respectively. The fit was
repeated until the root mean square (RMS) error of the fit was below 4/Ci with a maximum of
three repetitions but with completely random initial starting points within the accepted range
of the constraints. The length of the temporal window was set 273 ms (23 measurements),
which covers the duration of a typical saccade.
Saccade detection
Fig 5A shows 12 seconds of EOG recording together with derived parameters (Fig 5B)
Sx x Ci (Fig 5C) So (Fig 5D) Sg on the left y-axis. The most important parameter for saccade
detection was So. As a deflection in the EOG appeared in the temporal window, So
progressively increased from negative values and changed its sign to positive when the deflection
was in the middle of the window [
14
]. The second identifier of a saccade was its magnitude
Sx due to physiological limits of eye. Thus the largest accepted saccade was Nx,max, which
was set to 70Ê. The smallest accepted saccade (Nx,min) was a parameter likely to affect the
number of detected saccades. Therefore, the influence of this parameter was investigated as
a part of the study. The input for the detection algorithm were the parameters estimated at
the time t and t-1.
Fig 5. Detail of the saccade detection algorithm over 12 seconds of the experiment. An example of EOG recording
(A) and (B)-(D) estimated parameters Sx, So, and Sg. (B) Sx saccade magnitude parameter. (C) SoÐsaccade time shift
parameter. (D) SgÐsaccade gain parameter. Circles with lines show detected saccades and their magnitude (right
yaxis). The magnitude of a saccade was obtained by multiplying measured voltage Sx with Ci parameter obtained in the
training period.
9 / 24
Following a set of rules was used for saccade detection in each time t.
Sx;t
Sx;t 1
Ci 2 hNx;min; Nx;maxi
Ci 2 hNx;min; Nx;maxi So;t 2 0; 4=fsi So;t 1 < h 4=fs; 0i
The first and second conditions [(3) and (4)] define the boundaries for saccade magnitude
in the current estimate (at time t), and the estimate from the previous step (at time t-1). The
third and fourth conditions [(5) and (6)] define the zero-crossing time of parameter So
between t and t-1, and limit that time to be no farther than 4/fs from zero. Although it would
be possible to use more conditions and achieve better detection performance, or use a
statistically based model; here we aimed to demonstrate that a simple rule-based model is capable of
saccade detection, and restoring actual eye gaze angle.
Saccade integration
Saccade integration is a novel method of estimating eye gaze angle. It is based on an
assumption that in many real situations eye gaze behaviour can be characterized solely in terms of
saccades and fixations. It relies on the fact that eye positions resemble a normal distribution with
the mean in the midline of the visual field [
34
], and that eye positions are naturally limited.
The scheme is based on the step-like saccades (i.e. step changes) and stable fixations (i.e., no
movement). A simple summation of the saccades would be unstable because (a) the estimation
of saccade magnitude is noisy, (b) very small saccades cannot be detected, (c) the eye is not
stable during the fixation period, and (d) any detection algorithm on a noisy signal will always
have false alarms and misses. As a result, a simple summation of noisy estimates of saccades
would lead to integration errors (e.g., the estimates could depart from the natural boundaries).
One way of mitigating these problems is to represent the eye position as a Gaussian PDF
with the mean Xt,i and variance σ2t,i. If a saccade is detected, the magnitude of the new saccade
in degrees is added to the mean of the previous estimate.
3
4
5
6
7
8
9
10 / 24
where Xt-1,i is the previous estimate. The magnitude of saccade at time t is defined as
and the variance of the PDF increases by the measurement noise Nm:
X0t;i  Xt 1;i  saccEOG;t;i
saccEOG;t;i  sign Sg;t Sx;t
Ci
s0t2;i  st2 1;i  N2m
The new estimates of position (Xt,i) and variance (σ2t,i) are computed by simulation of the
newly obtained PDF, which is a truncated Gaussian distribution with the mean X't,i and
variance σ'2t,i clipped at the constraints EAmax = ±35Ê.
In order to characterize the saccade integration scheme, let us assume a perfectly
performing saccade detector. In our case, this was obtained from the video-based eye tracker. Hence,
there are two parameters Nm and Nx,min which influence the performance of the saccade
integration.
Fig 6. Limits of the saccade integration scheme. The figure shows the performance of the saccade integration scheme for
the current experiment assuming the perfect saccade detection. The r2 values of the estimated and actual eye gaze position
(yaxis) were computed for different values of Nm and Nx,min. The Nm is on the x-axis, Nx,min is represented by different types of
line. The lines show across-subject means; error bars show standard errors of the mean (SEM).
Fig 6 shows the effect of the Nm and Nx,min parameters on the performance of the saccade
integration scheme, with Nm on the x-axis and different line styles showing different values of
the Nx,min parameter. The performance (y-axis) was measured in the square of Person
product-moment correlation coefficients (r2) of the prediction versus the actual eye position. This
figure illustrates that in our dataset the maximum possible performance is r2 = 0.87 (Nx,min =
0Ê, Nm = 0Ê). This value decreases with increasing values of the investigated parameters.
Further, there is only a small difference between the lines Nx,min = 0Ê, and Nx,min = 4Ê. The line
representing Nx,min = 8Ê shows r2 values 0.71±0.76. The line representing Nx,min = 12Ê drops
even further to r2 values of approximately 0.64 with further decrease for small values of Nm.
The analysis determines the expected level of noise of the saccade integration scheme for
the perfect detector of saccades (without false alarms and misses). It also shows that if the
detector is capable of reliably estimating magnitudes and directions of saccades between 4±8Ê,
then it can estimate the actual eye gaze angle with the r2 more than 0.8.
Training
The algorithm required three input parameters that had to be calibrated using the ground
truth. The training period was defined as the first five minutes of the experiment after
stabilization of the HP filter with 0.01 Hz cut-off frequency; the training period lasted approximately
94 seconds. The current detection implementations had significant problems with rejecting
11 / 24
false alarms for steeply decreasing/increasing signals. Therefore the initial part of the signal
had to be discarded (see Sec. Results). The inputs for training were the EOG signal and the
ground truth. In the first step, the saccades were estimated from both the EOG and
videobased eye tracker. The EOG saccades were estimated with the current algorithm using a default
set of the parameters (fHP = 0.03 Hz, Nx,min = 6Ê, Nm = 10Ê, Ci = 700Ê/mV). In the second step,
the ground truth saccades were matched to the EOG based saccades and the parameter Ci was
estimated using a simple linear regression with one linear parameter. In the third step, the
algorithm was run again (fHP = 0.03 Hz and Ci set to a new value) for different values of the
Nm, and Nx,min parameters in order to find the optimal combination in terms of across-subject
mean r2 values. The values Nm = 9Ê and Nx.min = 8Ê represent the global maximum for the
current dataset. Subsequently, the estimated parameters Ci, Nm, and Nx,min were used to run the
algorithm on the data in the testing period.
Results
Raw data
The experiment was designed in order to characterize in-ear EOG measurements and to test
whether the saccade integration algorithm using only single-channel recordings could
reconstruct horizontal eye gaze angles.
Fig 1A and 1C show two samples of raw in-ear EOG recordings over 22 minutes. Fig 1B and
1D show the details of the EOG waveforms together with the positions of the visual targets.
These data illustrate the magnitude of the DC drift in comparison to the magnitude of the
EOG signal. Fig 1B demonstrates that the EOG signal correlates with the eye gaze angle and
that this relationship can be influenced by DC drift (Fig 1D). Fig 1D shows the case of high DC
drift, where it is more difficult to see the relationship between the EOG signal and the ground
truth. Transient events that relate to the saccades, however, are still visible in the raw data.
In-ear EOG
In order to characterize in-ear EOG and its relationship to eye movements, Fig 7 shows the
magnitude of change in the EOG signal as a function of the change of position in the visual
Fig 7. The change in the in-ear EOG as a function of the change of target angle. The magnitude of the change in the
visual target is shown on the x-axis. The change was defined as the difference between the medians of the
pretransition and post-transition periods. This was computed for each trial and each participant. Data of individual
participants are shown using thin grey lines, the across-subject mean value and SEM error bars are shown with the
dashed line.
12 / 24
target. Each thin grey line shows data from one participant, and the dashed line shows
acrosssubject means. For each transition of the target location, a 300 ms pre-transition to 600 ms
post-transition window was used, and the change in the EOG signal was defined as the median
value of the first 120 ms minus the median of the last 120 ms of the 900 ms period. The data
were pooled across initial target angles and repetitions, and medians were computed for each
magnitude of change. This method was preferred over using the linear regression, as in the
case of Ci computation, in order to avoid the assumptions of the current technique.
Fig 7 illustrates the linear relationship between the change of the target angle and the
change of EOG in the range of investigated eccentricities, confirming previous results [
16
]
when EOG was measured in the vicinity of eyes. The data also show that a change of 1Ê of
visual angle corresponded to 2.2 ± 0.5 μV (mean ± 95% CI). The across-subject variance could
be a consequence of various factors including the electrode contact, the shape of the head, and
the individual differences in the corneo-retinal potential (CRP). The CRP is the source of EOG
and it is known to vary with the luminance of the visual scene [
11
], but it can also be
influenced by individual differences in eye physiology.
Training performance
The performance of the whole algorithm was evaluated in terms of the parameters of a linear
model (standard deviation and gain) and the proportion of variance explained by the linear
model (r2). The saccade detection part of the algorithm was evaluated in terms of F-scores, a
measure which takes into account hits, misses, and false alarms [
10,15
]. The F-score is a
measure based on true positive rates (TPR), the percentage of true positives with respect to all true
events, and positive predictive values (PPV), the percentage of true positive events with respect
to all detected events by this method. The events were saccades obtained from the ground
truth measurements greater than Nx,min. Greater F indicates better detection; an F equal to 1
indicates perfect performance.
F  2
TRP PPV
TRP  PPV
10
The F-score does not take into account the magnitude and direction of the saccade. In
terms of our algorithm, the magnitudes of the saccades were important, because we aimed to
reconstruct the actual eye gaze angle by integrating saccades. Therefore, this measure was
introduced only to allow comparison with the previous work.
During the training period, the performance was evaluated at different values of the Nx,min
and Nm parameters. Fig 8 shows a subset of the training dataset for (Fig 8A±8D) Nm = 9Ê and
(Fig 8E±8G) Nx,min = 8Ê while varying the other parameter (fHP was set to 0.03 Hz). Nx,min is
the parameter of the detection step, thus the panel D shows how the F ratio was influenced by
this parameter. Nm is the parameter of the integration step; the detection was not influenced
by this parameter.
The upper row of Fig 8 shows that r2 peaks for the intermediate values of Nx,min, and it has
a maximum of 0.64. The standard deviation of error shows a similar but opposite pattern as r2;
the smallest value was 10Ê. The gain of the linear model is constant around a value of 1 for
Nx,min up to 10Ê and then decreases. On the other hand, the F-score increases monotonically
from ~0.49 at 0Ê to ~0.93 at 9Ê and then slowly increases further up to ~0.95 at 14Ê. The bottom
row shows similar patterns for the r2 (Fig 8E) and the error statistics (Fig 8F); however, the
gain statistic increases monotonically with Nm.
The upper row illustrates that it is beneficial to restrict the detection algorithm to saccades
of certain magnitude by setting the Nx,min parameter. The analysis also shows that the Nx,min
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Fig 8. Performance of SACCINT during the training period. The figure shows across-subject mean (±SEM)
performance as a function of Nx,min parameter (top row) and Nm parameter (bottom row). (A, E) The r2 values of the
actual and predicted eye angles, greater r2 indicates better performance. (B, F) the standard deviation of error of the
linear model. (C, G) The gain of the linear model. (D) Detection performance in F values (fHP = 0.03 Hz).
parameter mostly affects the error of the linear model. The bottom row shows that Nm
influences the slope of the estimated values. For example, the monotonic increase of the gain (Fig
8G) illustrates how the estimated eye positions become more `compressed' with greater Nm.
Gain < 1 indicates that the output values systematically undershoot the true values; gain > 1
indicates overshooting.
Testing performance
In this section, we compare the SACCINT algorithm against the traditional EOGHP approach
during the testing period for various cut-off frequencies. In order to obtain the output values
of eye positions, the HP filtered data were multiplied by Ci/2 and clipped at ±EAmax (±35Ê).
Fig 9 shows the performance of SACCINT for each participant (`x' symbol) versus the
performance of EOGHP as a function of fHP. The figure shows that `x' symbols lie above the
dashed lines in the most cases. One participant is below the dashed lines for certain fHP, and
one other participant is below the dashed line for fHP = 0.03 Hz. This suggests that our novel
algorithm SACCINT performs better than a simple HP filter (EOGHP) in most cases. The
performance of SACCINT improves with increasing performance of the HP filtering approach.
The results also demonstrate that the SACCINT approach is almost independent of the
value of fHP. The performance of some participants nearly approached the theoretical limit of
saccade integration. The difference between ideal performance (dotted horizontal line) and
the performance of the participants (`x' symbols) can be attributed only to the quality of the
detection step. Fig 9B also shows that the overall performance is limited by the measurements
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Fig 9. SACCINT vs. EOGHP. Data of individual participants are shown by `x' symbols. The x-axis shows the performance of the
EOGHP. Y-axis shows the performance of the SACCINT. Each panel shows data for single cut-off frequency of the HP filter. Solid lines
show predictions of the performance of SACCINT obtained from fitting a linear function on the individual data. The dotted line shows
the theoretical maximum of the saccade integration for the current set of parameters. The saccades were obtained from the video based
eye tracker were delayed by the time of half of the length of the temporal window for the purpose of this comparison and they were
integrated with the same parameters as the EOG based data; Nm = 9Ê and Nx,min = 8Ê.
of one particular participant. It is possible that the electrodes had poor contact during this
measurement which decreased the quality of the signal (see Sec. Errors in saccade detection).
The above observations can be summarized in the across-subject analysis of r2 (Fig 10A)
values and the analysis of RMS errors (Fig 10B). These data show that the saccade integration
Fig 10. Across-subject performance of SACCINT and EOGHP. (A) The left panel shows across-subject r2 values, separately for SACCINT (circles), EOGHP (squares),
and the ªidealº performance for the current set of parameters obtained from the ground truth (triangle) using the same parameters. The second and third columns show
the data without HP filtering. (B) The right panel shows across-subject RMS error using the same symbols.
15 / 24
scheme achieved maximum performance of r2 = 0.54 ± 0.14 (95% CI) for fHP = 0.01 Hz, and
the performance changed slightly with varying HP cut-off frequency. The across-subject
performance of the EOGHP was poor (r2 = 0) when no HP filter was applied. The performance
improved with increasing cut-off frequency and peaked at r2 = 0.46 for fHP = 0.03 Hz. It then
decreased for greater cut-off frequencies. The SACCINT performed better than the EOGHP
for some fHP but not all. SACCINT performed significantly better than EOGHP without the
HP filter (two-tailed paired t-test, t4 = 3.6244; p < 0.05, controlled for false discovery rate [
35
])
and with fHP = 0.01 Hz (t4 = 2.8886; p < 0.05).
The RMS error of the SACCINT had minimum 12Ê ± 2Ê (95% CI) for fHP = 0.01 Hz. The
performance was approximately constant for the set of investigated frequencies. The RMS
error of the EOGHP was 15Ê for fHP = 0.03 Hz and above, and this value was elevated for
decreasing the cut-off frequency. The only statistically significant difference between
SACCINCT and EOGHP was without HP filtering (t4 = 8.8034; p < 0.05).
These data illustrate that even EOGHP could predict eye gaze angle from in-ear EOG
measurements. The SACCINT algorithm is a more robust way of estimating the eye gaze angle
than the standard HP filtering. The performance of the EOGHP approach is strongly
influenced by the fHP value. The fact that EOGHP was not significantly different from SACCINT
for most fHP values partly relates to the design of the experiment. For example, fixation
periods > 1 s would deteriorate the EOGHP approach, but would not affect the new saccade
integration scheme SACCINT.
Errors in saccade detection
In order to analyse the detection algorithm of SACCINT, Fig 11 shows the patterns of errors of
a representative participant during the testing phase (fHP = 0.03 Hz). Panel Fig 11A shows that
computed saccades only slightly underestimated the magnitude of the actual saccades. When
the slope was fitted to the data of all participants, it had a value of 0.95 ± 0.05 (mean ± 95%
CI). This deviation from 1 relates to the selection of Nm = 9Ê in the training phase and the
cutoff frequency of the HP filter. The standard deviation of the error between the fit and the
matched saccades was 4.67Ê± 0.9 (across-subject mean ± 95% CI), which characterizes
highfrequency noise inherently present in the EOG signal and the precision of the saccade
magnitude estimation. Panel Fig 11B shows the relatively small number of misses and relatively large
Fig 11. Saccade detection evaluation for one participant. (A) Scatter plot of the computed versus the actual saccade magnitudes.
The solid line with open triangles shows the linear regression with the constant term fixed to zero. (B) Histogram of missed saccades,
the white bars show misses smaller than Nx,min (8Ê), the black bars show misses larger than Nx,min. (C) Histogram of false alarms.
White bars in the histogram show the data of saccades with magnitude smaller than Nx,min (8Ê), black bars show the rest of the
dataset. The numbers inside panels indicate a total number of points in each histogram. Subscript 1 refers to the black bars, and
subscript 2 refers to the white bars.
16 / 24
number of undetectable saccades, which suggests that the improvements in the saccade
detection algorithm may improve the performance. Fig 11C shows that the majority of the correct
rejections were of small magnitudes and they were filtered out at the detection step. Notably,
the algorithm still reports a substantial number of false alarms (276) which is 22% of all real
saccades.
Fig 12 provides further insight into the patterns of errors of the saccade detection
algorithm. The figure shows the temporal distributions of the misses and false alarms of the two
example participants whose raw EOG traces are shown in Fig 1. When Fig 12 is compared
with Fig 1 (Fig 12A corresponds to Fig 1A and 1B and Fig 12B corresponds to Fig 1C and 1D),
three characteristics of the algorithm's errors are shown. First, the number of false alarms
dramatically increased if the signal had a very strong DC component (Fig 1C) and contained
more high-frequency noise (Fig 1D). That is, the areas of densely distributed false alarms
being in one direction indicate that they had a common origin from the DC component; the
false alarms in both directions were present due to high-frequency noise. Second, the number
of misses was approximately constant. Third, many false alarms were due to the sloping signal
before the DC filter stabilised.
Taken all together, this indicates that the high false alarm rate was the most prominent
constraint of the current implementation. A proper statistical model of the eye movements (e.g.,
[
36
]) should eliminate the majority of the observed errors.
Discussion
The experiment and analysis demonstrated that it is possible to estimate horizontal eye gaze
angle using a single-channel EOG measurement with a pair of ear moulds positioned inside
the ear canal. However, the estimates are still noisy. SACCINT achieved the across-subject
performance of r2 = 0.54, which was better than a simple EOGHP approach for some values of
fHP. The performance of the EOGHP depends on the fixation period and the fHP, while
SACCINT is independent of the fixation period and much less dependent on fHP. Therefore, it is
likely that SACCINT would outperform the EOGHP in scenarios involving movements and
real visual targets once the saccade detection step is improved. However, only five participants
were tested in this study in a very controlled environment (e.g., with heads fixed), and with
custom-made electrodes. Therefore, the current results have to be understood in the context of
these and other limitations.
Firstly, the quality of the EOG measurements is critical for any EOG-based technology,
and it was observed that the quality varied across participants. This can be related to the quality
of our custom made electrodes, and it is very likely that better electrodes can substantially
improve this system.
Secondly, the analysis of errors showed that most of the errors were introduced by the
detection algorithm. Many of the errors could be eliminated by more advanced methods of
detection; for example, by probabilistic classification [
15
]. If the detection was ideal, the
performance could achieve an r2 of 0.8. One of the problems was that the current model could not
properly describe the drifting EOG signal (e.g., when the EOG was dominated by the DC drift,
or when the HP filter was introduced), because this type of signal was always incorrectly
interpreted as a series of saccades in one direction. This resulted in a large number of false alarms.
This particular problem limits the effectiveness of the algorithm. The number of false alarms
can be reduced in the future by modifying the model such that it captures the drift more
closely. The detection can be further improved by employing a more advanced model of eye
physiology [
36
] that, for example, assumes refectory periods between saccades and natural
rates of saccade occurrence, which can reduce the rate of false alarms. The statistics of eye
17 / 24
Fig 12. Temporal distribution of missed and falsely alarmed saccades of two example participants.
movements [
37
] and statistics of eye movements in relation to the eye position [
38,39
] could
also be implemented to improve the detection step. However, EOG does not contain any
information about the environment or the intention of the participant (e.g., whether the saccade is
voluntary or involuntary). Therefore any statistical model would have to take into account
only eye physiology, natural tendencies of the eye movements, or factors which are not
dependent on environment or task.
18 / 24
Thirdly, the integration step was a simplistic model of the eye physiology assuming a
perfectly constant eye position during the fixation and a step-like change of eye position during a
saccade. This introduced noise into the estimation process because the eye is never perfectly
still. Further, the additional noise was introduced because the estimated saccades were delayed
by approximately half of the duration of the window length. Implementing a statistical
predictor of the eye position, however, could improve the integration step. A possible future
predictor of the eye position is the head angle. The contributions of head movements to the eye gaze
directions have been previously demonstrated, for instance, in a visual search task experiment
[
34
] with stimuli distributed over 360Ê around the participant with unconstrained head
movements. That experiment showed that the distributions of the eye gaze directions followed the
distributions of the head vs. body orientation (e.g., when the head turns to left, the eye gaze is
likely to be to the left). That means that if the saccade integration model had access to the
actual head vs. body orientation, then it has an independent predictor of eye position.
However, the head was fixed in the current experiment, and the positions of the visual targets were
strictly controlled. Future experiments should, therefore, test the method in more realistic
environments that include head movements.
Relation to previous work
In-ear EOG. The magnitude of the in-ear EOG signal was estimated to be 2.2 μV per 1Ê
of visual angle, which is less than the measurements in the standard position and slightly less
than the previously reported in-ear measurement of 3 μV /1Ê [
18
]. One of the five
participants had an in-ear EOG magnitude of 2.8 μV/1Ê which is closer to the previous study. The
relationship of the change in EOG to the change in target angle was linear for the observed
transition magnitudes up to 61Ê. In our experiment, the saccade transitions were not
uniformly distributed, and the eye positions with eccentricities larger than 30.5Ê were not tested.
Therefore, further testing is necessary to establish whether linearity is preserved for extreme
eye positions.
Saccade detection and saccade identification. Previously, the saccades were detected by
analysing parameters of the continuous wavelet transformation [
10
]; the detector performed
with small number of errors (F = 0.94). In that study, they detected the magnitudes of the
saccades, but these were only classified as either small or large, and the actual eye angle was not
estimated. Barea et al. [
16
] reported that their system was able to identify saccades with
magnitudes greater than 10Ê and an error of 2Ê. A method of IaÂñez et al. [
14
] was based on an analysis
of the derivative of EOG. Detection performance was the same as [
11
] (F = 0.94). Another
method based on continuous wavelet transformation and auto-calibration [
21
] claimed almost
perfect detection of horizontal saccades, but the analysis was based on an offline artifact and
drift removal step. When the output was compared to the eye tracker data, the performance
diminished. Vidal et al. [
20
] based their method on feature extraction (velocity, acceleration,
slope, parameters of polynomial fit) and also claimed almost perfect detection. The study did
not report the length of the window that was used for the data analysis. Therefore, it was not
clear whether the data were processed offline or online. These various methods usually
achieved similar or better performance than our algorithm, but in all these studies, the EOG
signal was measured at the peri-orbital positions which offer a substantially higher signal to
noise ratio. The studies also tended to use signals from two or more channels (e.g., horizontal
and vertical channels), and they disregarded the magnitudes of the saccades when evaluating
the performance of the detection algorithm (e.g., a small saccade could be assigned as a large
saccade). Thus, it is not possible to directly compare the current results with the performance
of the mentioned methods.
19 / 24
Eye angle estimation. Several previous studies [
18,22,23,40,41
] have suggested the
possibility of estimating eye gaze angle from EOG. These methods either relied on readings from
multiple electrodes, or they used a camera for calibration. One approach [
22
] analysed the
EOG signal from multiple electrodes, which allowed to decorrelate the noise components in
different electrodes while preserving the EOG signal, thus allowing direct estimation of gaze
angle. In another approach [
23
], gaze angle estimation was based on the EOG signal that was
calibrated by saliency maps obtained from an external camera. The estimation RMS error of
the current method was 12Ê which is greater than the multiple-electrode method [
22
] error of
4Ê, but less than the externally calibrated method [
23
] error of 15Ê. However, the current and
the previous methods cannot be compared directly because neither of the previous
experiments measured the EOG signal inside the ear canals with just two electrodes.
Hearing aids and other applications
The motivation for the current investigation was the development of a portable and
unobtrusive eye gaze angle estimation technique for hearing aids. This could be used to steer
directional microphones toward attended sounds [
4
]. This technology could engage the
hearingimpaired listeners into dynamic conversations in noisy environments, and make such
situations less challenging because the listener usually consciously looks at the attended talker(s).
However, eye movements (as well as head movements) reflect exogenous attention which
might have a detrimental effect on listening, if the acoustic beam of the directional
microphone system was too narrow [
42
]. Therefore, future research is needed to estimate the effect
of the parameters of such technology on their benefit in real listening scenarios.
Potentially, eye-movement information could provide information about the health, mood,
or environment where the user currently is. For instance, previous research studied eye
movements in connection with various types of neurodegenerative disease [
43
]. Further, this type of
eye tracking could be incorporated in consumer headphones, virtual reality systems, or
systems that monitor fatigue. Portable eye tracking techniques have been previously used in
marketing [
44
], sport [
45
], sleep [
13
], and car driving [
46
] research. Less intrusive methods of eye
tracking could ease the data collection in realistic environments.
Limitations
The most notable limitation of all EOG applications is the signal to noise ratio, which relates
mainly to measurement artifacts: DC drift and muscular activity. The application is further
constrained by the assumptions of the current model, specifically its saccade detection and
integration. The algorithm is only capable of detecting (with relative reliability) saccades of
large magnitude (> 8Ê). The magnitude estimation, though, is accurate; mean estimation error
was 4.67Ê. The algorithm cannot detect smooth pursuit nor any other smooth eye movement.
Smooth pursuit and DC drift appear identical in the EOG signal, which means that they are
impossible to distinguish in an online analysis. Other limitations are the parameters of the
saccade integration model. In this work, these were estimated in the training period but in real
environments, they may change over time, and they need to be calibrated. The parameter Ci
may change with external lighting conditions. One possible solution is to implement a light
sensor and define the relationship between the change of lighting and in-ear EOG. However,
that would require an investigation of whether lighting is the only factor that affects the EOG
magnitude. A second way to calibrate Ci is to use the vestibulo-ocular reflex in connection
with head movements. When the head moves, eyes often remain fixed during head
movements, thus if the device was equipped with a gyroscope, then the strongly correlated outputs
of the EOG and gyroscope can instantaneously calibrate the system. Two other parameters Nm
20 / 24
and Nx,min are specific for this particular implementation, which means that they might need
to be replaced in the future. Moreover, Nm and Nx,min are not likely to change over time.
Another limitation of the current approach is that our tests were conducted only in one
controlled environment, with a small sample of participants, without deliberate body
movements, and with targets uniformly spaced across the visual field. Nevertheless, several
previous studies have demonstrated that EOG can be measured even in a mobile environment
[
9,10,23
], and showed that specialized algorithms can diminish the effects of commonly
occurring artifacts (e.g., the walking artifact). Certain artifacts cannot be filtered easily. For
example, the artifacts related to the jaw or tongue movements would be difficult to filter,
because they do not have any regular shape or frequency, and any EOG-to-gaze algorithm is
vulnerable to them.
The current algorithm can be used online, but this analysis was run offline on a PC with
high computational power. In this implementation, the most computationally demanding step
is the non-linear fitting procedure, but a different fitting procedure may be more
computationally efficient. One further limitation is that the current approach analysed the signal in a
temporal window, which in practice would lead to a delay up to 200 ms, and this delay cannot be
avoided.
Conclusion
The current work showed that it is possible to estimate the eye gaze angle with a single-channel
in-ear EOG recording using EOGHP (r2 = 0.46) and a novel SACCINT (r2 = 0.54) method.
The estimates were still noisy, but in theory the SACCINT could attain much better
performance (r2 > 0.8). This difference between the theory and the actual performance of the
SACCINT can be attributed mostly to the quality of the in-ear EOG signal, which lead to errors in
the detection and integration steps. Therefore, further improvements of this method are
necessary. A number of improvements have been proposed, including improving the design of the
electrodes, improving the non-linear fitting procedure, modelling of eye physiology,
incorporating gyroscope signals, or incorporating statistical models. Overall, our investigation suggests
that in-ear EOG signals captured with conductive ear moulds could serve as a basis for
lightweight, portable horizontal eye gaze angle estimation suitable for broad range of applications
not limited to hearing aids.
Acknowledgments
We wish to acknowledge Dr. William `Bill' Whitmer for his helpful suggestions and
comments.
Conceptualization: ĽuboÏs HlaÂdek, Bernd Porr, W. Owen Brimijoin.
Data curation: ĽuboÏs HlaÂdek.
Formal analysis: ĽuboÏs HlaÂdek.
Funding acquisition: Bernd Porr, W. Owen Brimijoin.
Investigation: ĽuboÏs HlaÂdek, Bernd Porr, W. Owen Brimijoin.
Methodology: ĽuboÏs HlaÂdek, Bernd Porr, W. Owen Brimijoin.
Project administration: W. Owen Brimijoin.
Resources: Bernd Porr, W. Owen Brimijoin.
21 / 24
Software: Bernd Porr.
Supervision: Bernd Porr, W. Owen Brimijoin.
Writing ± original draft: ĽuboÏs HlaÂdek.
Writing ± review & editing: Bernd Porr, W. Owen Brimijoin.
22 / 24
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